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Journals and Conferences
Some characterizations of the Euclidean rectifying curves, i.e. the curves in E which have a property that their position vector always lies in their rectifying plane, are given in . In this paper, we characterize non–null and null rectifying curves, lying fully in the Minkowski 3–space E 1 . Also, in considering a causal character of a curve we give… (More)
In this paper, we characterize the spacelike, the timelike and the null rectifying curves in the Minkowski 3-space in terms of centrodes. In particular, we show that the spacelike and timelike rectifying curves are the extremal curves for which the corresponding function takes its extremal value. On the other hand, we also show that the null rectifying… (More)
1 Department of Mathematics, Faculty of Sciences, University of Cankiri Karatekin, Cankiri 18100, Turkey 2 School of Mathematics & Statistical Sciences, Arizona State University, Room PSA442, Tempe, AZ 85287-1804, USA 3Department of Mathematics, Faculty of Sciences and Art, University of Kırıkkale, Kırıkkale 71450, Turkey 4University of Kragujevac, Faculty… (More)
We define normal curves in Minkowski space-time E4 1 . In particular, we characterize the spacelike normal curves in E4 1 whose Frenet frame contains only non-null vector fields, as well as the timelike normal curves in E4 1 , in terms of their curvature functions. Moreover, we obtain an explicit equation of such normal curves with constant curvatures.
In this paper, we define Mannheim partner curves in three dimensional dual space D and we obtain the necessary and sufficient conditions for the Mannheim partner curves in dual space D.
We define generalized null Mannheim curves in Minkowski spacetime and characterize them and their generalized Mannheim mate curves in terms of curvature functions, and obtain relations between their frames. We provide examples of such curves.
In this paper, by using the similar idea of Matsuda and Yorozu , we prove that if bitorsion of a quatenionic curve α is no vanish, then there is no quaternionic curve in E is a Bertrand curve. Then we define (1, 3) type Bertrand curves for quatenionic curve in Euclidean 4-space. We give some characterizations for a (1, 3) type quaternionic Bertrand… (More)
In this study, we have investigated the possibility of whether any Frenet plane of a given space curve in a 3-dimensional Euclidean space Ealso is any Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.